You can't disable it to get back some more screen real estate, but you can change its colour so that it "disappears"...

Add the following to your .screenrc:

caption string "%{kk}XXXXXXX"

So, how does this work? Well assuming your screen terminal background is black, you are making the caption strings background and foreground black as well. "k" stands for black, the first is for the foreground and the second one is for the background. The "XXXXXX"s are simply a string to make it work.

I guess if you have chosen a different background colour for your main terminal, you simply change kk to whatever colour you have chosen. Yes, you get a small gap, but not as in your face as the big bars across the screen.